The Dow Jones Industrial Average (DJIA) and the Standard &...

The Dow Jones Industrial Average (DJIA) and the Standard \& Poor's 500 Index (S\&P 500$)$ . are both used to measure the performance of the stock market. The DJIA is based on the price of stocks for 30 large companies; the S\&P 500 is based on the price of stocks for 5000 companies. If both the DJIA and S\&P 500 measure the performance of the stock market, how are they correlated? The following data show the daily percent increase or daily percent decrease in the DJIA and S\&P 500 for a sample of nine days over a three-month period (The Wall Street Journal, January 15 to March $10,2006 )$ a. Show a scatter diagram. b. Compute the sample correlation coefficient for these data. c. Discuss the association between the DJIA and S\&P 500. Do you need to check both before having a general idea about the daily stock market performance?

The Dow Jones Industrial Average (DJIA) and the Standard \& Poor's 500 Index (S\&P 500$)$ .
are both used to measure the performance of the stock market. The DJIA is based on the price of stocks for 30 large companies; the S\&P 500 is based on the price of stocks for 5000
companies. If both the DJIA and S\&P 500 measure the performance of the stock market, how are they correlated? The following data show the daily percent increase or daily
percent decrease in the DJIA and S\&P 500 for a sample of nine days over a three-month period (The Wall Street Journal, January 15 to March $10,2006 )$
a. Show a scatter diagram.
b. Compute the sample correlation coefficient for these data.
c. Discuss the association between the DJIA and S\&P 500. Do you need to check both
before having a general idea about the daily stock market performance?

Key Concepts

Scatter Diagram

A scatter diagram is a graphical representation that displays values for two variables as points on a coordinate system. It is used to visually inspect the relationship, trend, and potential correlation between the variables, helping to identify patterns or outliers in the data.

Correlation Coefficient

The correlation coefficient is a statistical measure that quantifies the degree to which two variables are linearly related. It provides a value ranging from -1 to 1, where values near 1 signify a strong positive relationship, values near -1 indicate a strong negative relationship, and values closer to 0 imply little to no linear association.

Association

Association in the context of statistics refers to the connection or relationship between two variables. It indicates whether an increase or decrease in one variable tends to be accompanied by an increase or decrease in another variable, aiding in understanding patterns or linkages within data.

Stock Market Indices

Stock market indices are composite measures that track the performance of a selected group of stocks, representing a segment or the overall market. They serve as benchmarks to gauge market trends, investor sentiment, and the economic health reflected in the performance of the included companies.

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